In conventional solutions, such as that illustrated in FIGS. 1 and 2 (see for example FR-A-2.507.266 and FR-A-2.218.501), the two segments 1 and 3 of the shaft--which have a non-circular profile and the possibility of sliding in relation to one another--are connected to forks 5 and 7 respectively by means of pins 9 and 10 respectively, which pass through axial seats formed in the forks 5 and 7, in which seats the ends of the segments 1 and 3 respectively are received. These seats can have a shape corresponding to that of the segments 1 and 3 for angular coupling. On the outside of the bases 5A and 7A of the forks 5 and 7, that is to say at the opposite end to the arms 5B and 7B of the forks, there is an annular channel 5C and 7C respectively, which channels partly contain sliding blocks 12A and 14A respectively which form part of protective boots 12 and 14 for the cardan joints of which the forks 5 and 7 respectively form part. Integral with the protective boots 12 and 14 are protective sleeves 16 and 18 respectively which are coupled in a telescopically slidable manner and which are connected rotatably to the boots 12 and 14 respectively. By preventing the protective means constituted by the boots 12 and 14 and by the tubular sleeves 16 and 18 from rotating, the shaft constituted by the forks 5 and 7 and by the segments 1 and 3 can rotate, the surfaces of the channels 5C and 7C sliding relative to the sliding blocks 12A and 14A which support the protective means 12, 16, 18, 14 defined above. The sliding blocks 12A and 14A which support the protective sleeve on the rotating shaft are located practically at the ends of the forks and at the ends of the associated protective boots. The supports of the boots 12 and 14--which are constituted by these sliding blocks 12A and 14A--are therefore positioned virtually at the inner end of the respective protective boots 12 and 14 which project unsupported from the support sliding blocks 12A and 14A over the forks 5 and 7 and therefore over the cardan joints of which the arms 5B and 7B of the forks 5 and 7 form part. It follows from this that a load bearing down in the direction of arrow fc has to be supported directly by the structure of the respective boot such as 12 which in this case tends to be deformed until it actually comes into contact with the arms of the fork such as 5B of the fork 5, the result of which is a dangerous tendency of the shaft to pull round with it all the protective means constituted by the boots and by the sleeves, thus neutralizing the protective effect. The most recent standards aimed at countering the danger of accidents provide for stringent tests to prevent the abovementioned risks, and the aim of the invention is to modify the conventional structures represented in FIGS. 1 and 2 in order to achieve greater protective effectiveness of the protective sleeves without greatly affecting the robustness and other strength characteristics which otherwise have to be provided exclusively by the shape of the boots. These and other aims and advantages will become clear from reading the following text.